Hello Yann, great that the heads are working – you can get on and recover the tapes now. A good clean of the tape transport with IPA may be worth doing before going too far.
Re your interconnect issue, it is also possible to send the audio out to the RADIO DIN socket if the press buttons are used. That socket is wired mirror image to the line socket, so it will work with your cable. The function diagram for BEOCORD 2000 DE LUXE is a help, it shows the line out as pins 1 & 4 on the LINE socket, but 3 & 5 on the RADIO socket.
Regarding the transport noise, my experience is a small drop of oil on the transport wheel shafts and I can’t hear the mechanical noise over the noise from a clothes washing machine 2 rooms away – not silent, but I would say quiet.
Good luck.